For each sequence $a_n$ find a number k such that $n^k a_n$
has a finite non-zero limit.
(This is of use, because by the limit comparison test the series $\displaystyle \sum_{n=1}^\infty a_n$ and $\displaystyle \sum_{n=1}^\infty n^{-k}$ both converge or both diverge.)
A. $a_n = (3 + 5 n)^{- 3}$
k =

B. $a_n = \frac{3}{n^{6} + n}$
k =

C. $a_n = \frac{7 n^2 + 3 n + 7 }{6 n^{6 } + 6 n + 5 }$
k =

D. $a_n = \left( \frac{7 n^2 + 3 n + 3 }{6 n^{6 } + 6 n + 5 \sqrt n } \right) ^{3 }$
k =